A jet pilot takes his aircraft in a vertical loop.
A) If the jet is moving at a speed of 1300 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 5.0 g’s.
B) Calculate the 78 kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle.
C) Calculate the 78 kg pilot’s effective weight (the force with which the seat pushes up on him) at the top of the circle (assume the same speed).
1 Answer

V = 1300 km/h = 1300(1000/3600) = 361 m/s
Ac = Centripetal Acceleration = V²/R
5g = (361)²/R
R = (361)²/5(9.81) = 2660 m ANS A)
At bottom of circle => Normal force = mAc + mg = m(361)²/2660 + m(9.81)
Normal force = 49.0m + 9.81m = 58.8(78) = 4590 N ANS B)
At top of circle => Normal force = mAc – mg = 49.0 m – 9.81m = 39.2m
Normal force = 39.2(78) = 3060 N ANS C)